Non-equilibrium Phase Separation Research Articles

A Microfluidic and Numerical Analysis of Non-equilibrium Phase Behavior of Gas Condensates

Conventional assumptions about multiphase flow in gas condensate reservoirs often do not correlate with field production. This discrepancy stems from the various mechanisms influencing the multiphase process, which are inadequately represented in numerical models. One of the least understood mechanisms is the influence of the non-equilibrium thermodynamics on the flow in the wellbore region, where the reservoir pressure is below the dew point pressure. To address this problem, experimental and mathematical analyses were conducted using a microfluidic device designed to replicate the flow dynamics in a gas condensate system. The experimental results showed an 11% deviation from the initial pressure of condensate saturation when compared with the conventional assumption of local equilibrium in numerical models. Similarly, there is a 14% deviation between the experimental and simulated volumes of the condensate. These findings underscore the inadequacy of existing models to accurately predict the saturation profile of the condensate phase. A mathematical model based on a relaxation parameter was applied to account for non-equilibrium phase separation and the fog state of the aerosol as observed in the microfluidic experiment. Incorporating a relaxation parameter (τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au$$\\end{document}) enhanced the accuracy of the prediction of the initial pressure of the condensate saturation and an improvement in the prediction of the condensate volumes from 76% to 97.2%. Consequently, it provides a valuable framework and insight on the non-equilibrium phase behavior of gas condensate systems under constant flow regimes.

Universal properties of repulsive self-propelled particles and attractive driven particles

Motility-induced phase separation (MIPS) is a nonequilibrium phase separation that has a different origin from equilibrium phase separation induced by attractive interactions. Similarities and differences in collective behaviors between these two types of phase separation have been intensely discussed. Here, to study another kind of similarity between MIPS and attraction-induced phase separation under a nonequilibrium condition, we perform simulations of active Brownian particles with uniaxially anisotropic self-propulsion (uniaxial ABPs) in two dimensions. We find that (i) long-range density correlation appears in the homogeneous state; (ii) anisotropic particle configuration appears in MIPS, where the anisotropy removes the possibility of microphase separation suggested for isotropic ABPs [X.-Q. Shi , ]; and (iii) critical phenomena for the anisotropic MIPS presumably belong to the universality class for two-dimensional uniaxial ferromagnets with dipolar long-range interactions. Properties (i)–(iii) are common to the well-studied randomly driven lattice gas (RDLG), which is a particle model that undergoes phase separation by attractive interactions under external driving forces, suggesting that the origin of phase separation is not essential for macroscopic behaviors of uniaxial ABPs and RDLG. Based on the observations in uniaxial ABPs, we construct a coarse-grained Langevin model that shows properties (i)–(iii) and corroborates the generality of the findings. Published by the American Physical Society 2024

Fluctuations and Shape Dependence of Microphase Separation in Systems with Long-Range Interactions.

The combination of phase separation and long-ranged, effective, Coulomb interactions results in microphase separation. We predict the sizes and shapes of such microdomains and uniquely their dependence on the macroscopic sample shape which also affects the effective interfacial tension of fluctuations of the lamellar phase. These are applied to equilibrium salt solutions and block copolymers. Nonequilibrium phase separation in the presence of chemical reactions (e.g., cellular condensates) is mapped to the Coulomb theory to which our predictions apply. In some cases, the effective interfacial tension can be ultralow.

Operando monitoring of single-particle kinetic state-of-charge heterogeneities and cracking in high-rate Li-ion anodes

To rationalize and improve the performance of newly developed high-rate battery electrode materials, it is crucial to understand the ion intercalation and degradation mechanisms occurring during realistic battery operation. Here we apply a laboratory-based operando optical scattering microscopy method to study micrometre-sized rod-like particles of the anode material Nb14W3O44 during high-rate cycling. We directly visualize elongation of the particles, which, by comparison with ensemble X-ray diffraction, allows us to determine changes in the state of charge of individual particles. A continuous change in scattering intensity with state of charge enables the observation of non-equilibrium kinetic phase separations within individual particles. Phase field modelling (informed by pulsed-field-gradient nuclear magnetic resonance and electrochemical experiments) supports the kinetic origin of this separation, which arises from the state-of-charge dependence of the Li-ion diffusion coefficient. The non-equilibrium phase separations lead to particle cracking at high rates of delithiation, particularly in longer particles, with some of the resulting fragments becoming electrically disconnected on subsequent cycling. These results demonstrate the power of optical scattering microscopy to track rapid non-equilibrium processes that would be inaccessible with established characterization techniques.

Anomalous phase separation in a correlated electron system: Machine-learning–enabled large-scale kinetic Monte Carlo simulations

SignificancePhase separation is crucial to the functionalities of many correlated electron materials with notable examples including colossal magnetoresistance in manganites and high-Tc superconductivity in cuprates. However, the nonequilibrium phase-separation dynamics in such systems are poorly understood theoretically, partly because the required multiscale modeling is computationally very demanding. With the aid of machine-learning methods, we have achieved large-scale dynamical simulations in a representative correlated electron system. We observe an unusual relaxation process that is beyond the framework of classical phase-ordering theories. We also uncover a correlation-induced freezing behavior, which could be a generic feature of phase separation in correlated electron systems.

Activity-driven topological glass

1. Active topological glass Authors: Jan Smrek, Iurii Chubak, Christos N. Likos, and Kurt Kremer Nature Communications, 11: 26, 2020; DOI: 10.1038/s41467-019-13696-z 2. Emergence of active topological glass through directed chain dynamics and nonequilibrium phase separation Authors: Iurii Chubak, Christos N. Likos, Kurt Kremer, and Jan Smrek Physical Review Research, 2: 043249, 2020; DOI: 10.1103/PhysRevResearch.2.043249 […]

A novel jamming phase diagram links tumor invasion to non-equilibrium phase separation

SummaryIt is well established that the early malignant tumor invades surrounding extracellular matrix (ECM) in a manner that depends upon material properties of constituent cells, surrounding ECM, and their interactions. Recent studies have established the capacity of the invading tumor spheroids to evolve into coexistent solid-like, fluid-like, and gas-like phases. Using breast cancer cell lines invading into engineered ECM, here we show that the spheroid interior develops spatial and temporal heterogeneities in material phase which, depending upon cell type and matrix density, ultimately result in a variety of phase separation patterns at the invasive front. Using a computational approach, we further show that these patterns are captured by a novel jamming phase diagram. We suggest that non-equilibrium phase separation based upon jamming and unjamming transitions may provide a unifying physical picture to describe cellular migratory dynamics within, and invasion from, a tumor.

Non-equilibrium phase separation in mixtures of catalytically active particles: size dispersity and screening effects

Biomolecular condensates in cells are often rich in catalytically active enzymes. This is particularly true in the case of the large enzymatic complexes known as metabolons, which contain different enzymes that participate in the same catalytic pathway. One possible explanation for this self-organization is the combination of the catalytic activity of the enzymes and a chemotactic response to gradients of their substrate, which leads to a substrate-mediated effective interaction between enzymes. These interactions constitute a purely non-equilibrium effect and show exotic features such as non-reciprocity. Here, we analytically study a model describing the phase separation of a mixture of such catalytically active particles. We show that a Michaelis–Menten-like dependence of the particles’ activities manifests itself as a screening of the interactions, and that a mixture of two differently sized active species can exhibit phase separation with transient oscillations. We also derive a rich stability phase diagram for a mixture of two species with both concentration-dependent activity and size dispersity. This work highlights the variety of possible phase separation behaviours in mixtures of chemically active particles, which provides an alternative pathway to the passive interactions more commonly associated with phase separation in cells. Our results highlight non-equilibrium organizing principles that can be important for biologically relevant liquid-liquid phase separation.Graphic abstract

Plasma assisted molecular beam epitaxy growth mechanism of AlGaN epilayers and strain relaxation on AlN templates

Several series of high Al composition AlGaN epilayers were grown on AlN/sapphire templates by plasma assisted molecular beam epitaxy. Three growth regions, Ga droplets, intermediate Ga-rich, and N-rich, have been identified based on in situ and various ex situ characterizations, and AlGaN growth diagrams have been summarized. The Al composition is basically determined by Al supply when it is less than the effective N radical beam supply. X-ray diffraction reciprocal space maps have revealed residual strain status of AlGaN on AlN, demonstrating lattice relaxation as the layer thickness increases. The experimental critical thicknesses are observed increasing as Al composition increases, but they deviate from the theoretical values, which is attributed to the combined influence of nonequilibrium growth conditions, kinetics, phase separation and dislocation generation. Energy bandgaps were determined by optical absorption edges, suggesting a bowing parameter of 1.1 eV.

Phase mechanics of colloidal gels: osmotic pressure drives non-equilibrium phase separation.

Although dense colloidal gels with interparticle bonds of order several kT are typically described as resulting from an arrest of phase separation, they continue to coarsen with age, owing to the dynamics of their temporary bonds. Here, k is Boltzmann's constant and T is the absolute temperature. Computational studies of gel aging reveal particle-scale dynamics reminiscent of condensation that suggests very slow but ongoing phase separation. Subsequent studies of delayed yield reveal structural changes consistent with re-initiation of phase separation. In the present study we interrogate the idea that mechanical yield is connected to a release from phase arrest. We study aging and yield of moderately concentrated to dense reversible colloidal gels and focus on two macroscopic hallmarks of phase separation: increases in surface-area to volume ratio that accompanies condensation, and minimization of free energy. The interplay between externally imposed fields, Brownian motion, and interparticle forces during aging or yield, changes the distribution of bond lengths throughout the gel, altering macroscopic potential energy. The gradient of the microscopic potential (the interparticle force) gives a natural connection of potential energy to stress. We find that the free energy decreases with age, but this slows down as bonds get held stretched by glassy frustration. External perturbations break just enough bonds to liberate negative osmotic pressure, which we show drives a cascade of bond relaxation and rapid reduction of the potential energy, consistent with renewed phase separation. Overall, we show that mechanical yield of reversible colloidal gels releases kinetic arrest and can be viewed as non-equilibrium phase separation.

Self-generated persistent random forces drive phase separation in growing tumors.

A single solid tumor, composed of nearly identical cells, exhibits heterogeneous dynamics. Dynamics of cells in the core is glass-like, whereas those in the periphery undergoes diffusive or super-diffusive behavior. Quantification of heterogeneity using the mean square displacement or the self-intermediate scattering function, which involves averaging over the cell population, hides the complexity of the collective movement. Using the t-distributed stochastic neighbor embedding (t-SNE), a popular unsupervised machine learning dimensionality reduction technique, we show that the phase space structure of an evolving colony of cells, driven by cell division and apoptosis, partitions into nearly disjoint sets composed principally of the core and periphery cells. The non-equilibrium phase separation is driven by the differences in the persistence of self-generated active forces induced by cell division. Extensive heterogeneity revealed by t-SNE paves the way toward understanding the origins of intratumor heterogeneity using experimental imaging data.

Emergence of active topological glass through directed chain dynamics and nonequilibrium phase segregation

This work shows how glassy behavior emerges from the active, directed polymer dynamics that is triggered by the non-equilibrium phase separation.

Preparation of Cellulose Particles with a Hollow Structure.

In this study, we report the preparation of hollow cellulose particles via a solvent-releasing method with the ionic liquid 1-ethyl-3-methylimidazolium acetate ([Emim]Ac). A dispersion comprising [Emim]Ac droplets with dissolved cellulose and a hexane medium containing a stabilizer was poured into a large amount of acetone (precipitant), resulting in the precipitation of cellulose and the formation of solid cellulose particles with a hollow structure. We found that the formation of the hollow structure resulted from the equilibrium phase separation. Porous structures were also obtained using ethanol or t-butanol as a precipitant, where cellulose immediately precipitated (i.e., exhibited non-equilibrium phase separation). In the case where acetone was used as the precipitant, the diffusion rate of [Emim]Ac from the droplets into the precipitant was relatively low; that is, the precipitation of cellulose was delayed, which allowed the cellulose to be phase-separated into a thermodynamically stable structure (equilibrium phase separation), resulting in the formation of the hollow structure.

Non-equilibrium phase separation with reactions: a canonical model and its behaviour

Materials undergoing both phase separation and chemical reactions (defined here as all processes that change particle type or number) form an important class of non-equilibrium systems. Examples range from suspensions of self-propelled bacteria with birth–death dynamics, to bio-molecular condensates, or ‘membraneless organelles’, within cells. In contrast to their passive counterparts, such systems have conserved and non-conserved dynamics that do not, in general, derive from a shared free energy. This mismatch breaks time-reversal symmetry and leads to new types of dynamical competition that are absent in or near equilibrium. We construct a canonical scalar field theory to describe such systems, with conserved and non-conserved dynamics obeying model B and model A, respectively (in the Hohenberg–Halperin classification), chosen such that the two free energies involved are incompatible. The resulting minimal model is shown to capture the various phenomenologies reported previously for more complicated models with the same physical ingredients, including microphase separation, limit cycles and droplet splitting. We find a low-dimensional subspace of parameters for which time-reversal symmetry is accidentally recovered, and show that here the dynamics of the order parameter field (but not its conserved current) is exactly the same as an equilibrium system in which microphase separation is caused by long-range attractive interactions.

Intrinsically disordered proteins access a range of hysteretic phase separation behaviors.

The phase separation behavior of intrinsically disordered proteins (IDPs) is thought of as analogous to that of polymers that undergo equilibrium lower or upper critical solution temperature (LCST and UCST, respectively) phase transition. This view, however, ignores possible nonequilibrium properties of protein assemblies. Here, by studying IDP polymers (IDPPs) composed of repeat motifs that encode LCST or UCST phase behavior, we discovered that IDPs can access a wide spectrum of nonequilibrium, hysteretic phase behaviors. Experimentally and through simulations, we show that hysteresis in IDPPs is tunable and that it emerges through increasingly stable interchain interactions in the insoluble phase. To explore the utility of hysteretic IDPPs, we engineer self-assembling nanostructures with tunable stability. These findings shine light on the rich phase separation behavior of IDPs and illustrate hysteresis as a design parameter to program nonequilibrium phase behavior in self-assembling materials.

Interfacial Properties of Active-Passive Polymer Mixtures.

Active matter consists of particles that dissipate energy, from their own sources, in the form of mechanical work on their surroundings. Recent interest in active-passive polymer mixtures has been driven by their relevance in phase separation of (e.g., transcriptionally) active and inactive (transcriptionally silent) DNA strands in nuclei of living cells. In this paper, we study the interfacial properties of the phase separated steady states of the active-passive polymer mixtures and compare them with equilibrium phase separation. We model the active constituents by assigning them stronger-than-thermal fluctuations. We demonstrate that the entropy production is an accurate indicator of the phase transition. We then construct phase diagrams and analyze kinetic properties of the particles as a function of the distance from the interface. Studying the interface fluctuations, we find that they follow the capillary waves spectrum. This allows us to establish a mechanistic definition of the interfacial stiffness and its dependence on the relative level of activity with respect to the passive constituents. We show how the interfacial width depends on the activity ratio and comment on the finite size effects. Our results highlight similarities and differences of the non-equilibrium steady states with an equilibrium phase separated polymer mixture with a lower critical solution temperature. We present several directions in which the non-equilibrium system can be studied further and point out interesting observations that indicate general principles behind the non-equilibrium phase separation.

Environmental adaptivity of the surface of styrene-isoprene-styrene tri-block copolymers films controlled by the film-preparation kinetics

The responses of the surface structures to the solvent vapor treatment for the films of styrene(S)/ isoprene(I)/styrene(S) tri-block copolymers (SIS) prepared by various casting solvents and film-formation methods (solvent-casting and spin-coating) were investigated by contact angle measurement, atomic force microscopy (AFM) and sum frequency generation vibrational spectroscopy (SFG). It was shown that the surface wettability of the SIS solvent-cast films (cyclohexanone as solvent) and spin-coated films (toluene as solvent) exhibited the reversibly switching properties, if alternately exposed them to the vapor of PI-selective (cyclohexane) and PS-selective (butanone) solvents. However, for the solvent-cast films prepared by cyclohexane and toluene solution, the wettability of the films surface did not change, regardless of which solvent was applied in vapor treatment. It was claimed that the difference in the phase-separation structure of the SIS films prepared using different casting solvents and film-formation methods is the main reason for the discrepancy in the surface adaptive behavior. If the films have the equilibrium phase structures, the energy barrier for the conformation adjustment is apparently larger, and therefore it is hard to change the aggregation structure to accommodate the new solvent-vapor environment. While for the films having the non-equilibrium phase-separation structures, the conformational adjustment under the different solvent vapor will become relatively easier. Owing to this effect, the prepared SIS films with various film-formations kinetics can form different aggregation structures after a specific solvent vapor treatment, and finally leads to dissimilar surface structure. As a result, the surface wettability of these films exhibit different responsiveness to solvent vapor.

An aggregation-removal model for the formation and size determination of post-synaptic scaffold domains

The formation and stability of synapses are key questions in neuroscience. Post-synaptic domains have been classically conceived as resulting from local insertion and turnover of proteins at the synapse. However, insertion is likely to occur outside the post-synaptic domains and advances in single-molecule imaging have shown that proteins diffuse in the plane of the membrane prior to their accumulation at synapses. We quantitatively investigated this scenario using computer simulations and mathematical analysis, taking for definiteness the specific case of inhibitory synapse components, i.e., the glycine receptor (GlyR) and the associated gephyrin scaffolding protein. The observed domain sizes of scaffold clusters can be explained by a dynamic balance between the aggregation of gephyrin proteins diffusing while bound to GlyR and their turnover at the neuron membrane. We also predict the existence of extrasynaptic clusters with a characteristic size distribution that significantly contribute to the size fluctuations of synaptic domains. New super-resolution data for gephyrin proteins established the existence of extrasynaptic clusters the sizes of which are consistent with the model predictions in a range of model parameters. At a general level, our results highlight aggregation with removal as a non-equilibrium phase separation which produces structures of tunable size.

Motility-induced phase separation in an active dumbbell fluid

We study a suspension of active dumbbells of variable density, as a minimal example of an active polar fluid. As in a fluid of spherical swimmers, we find that motility triggers a nonequilibrium phase separation if the density exceeds a critical threshold. We also show that the phase separation is lost when the active force becomes too large, ultimately due to inertial effects. Remarkably, the aggregates which assemble spontaneously break chiral symmetry and rotate; they also display a nematic ordering with spiral patterns.

Clustering and heterogeneous dynamics in a kinetic Monte Carlo model of self-propelled hard disks.

We introduce a kinetic Monte Carlo model for self-propelled hard disks to capture with minimal ingredients the interplay between thermal fluctuations, excluded volume, and self-propulsion in large assemblies of active particles. We analyze in detail the resulting (density, self-propulsion) nonequilibrium phase diagram over a broad range of parameters. We find that purely repulsive hard disks spontaneously aggregate into fractal clusters as self-propulsion is increased and rationalize the evolution of the average cluster size by developing a kinetic model of reversible aggregation. As density is increased, the nonequilibrium clusters percolate to form a ramified structure reminiscent of a physical gel. We show that the addition of a finite amount of noise is needed to trigger a nonequilibrium phase separation, showing that demixing in active Brownian particles results from a delicate balance between noise, interparticle interactions, and self-propulsion. We show that self-propulsion has a profound influence on the dynamics of the active fluid. We find that the diffusion constant has a nonmonotonic behavior as self-propulsion is increased at finite density and that activity produces strong deviations from Fickian diffusion that persist over large time scales and length scales, suggesting that systems of active particles generically behave as dynamically heterogeneous systems.